Soliton distillation is applied to pulses with different peak powers from a fiber laser. A specific normalization strategy is adopted to check the influence on soliton purification. During soliton distillation, we used the same normalization parameter, instead of individual optimized normalization parameters, for pulses with different peak powers, even for pulses with peak power differences larger than 3 dB. Simulation results suggest that the nonlinear Fourier transform can be performed by using the same normalization parameter for pulses of different intensities. The discrete spectrum energy of the purified soliton can be used to quantify the degree of deviation from the original pulse.